The prior work of Li et al.~\cite{SPAA10,ASAP10} used the
number of dummy messages to judge the effectiveness of their
techniques, making the assumption that dummy message
volume at least correlates to overall application performance.
Here, we provide empirical
evidence that the number of dummy messages can indeed have
a tangible impact on overall application performance.

Consider the application topology of Figure~\ref{fig:splitjoin}.
Li et al.~\cite{ASAP10} described a pseudo-random number generator
with this toplogy in which node $A$ generates uniformly distributed
random numbers and nodes $B$ and $C$ transform those uniform variates
into normally distributed random numbers via a rejection method.
The Marsaglia polar method quoted in~\cite{ASAP10}
filters approximately 21\% of its inputs.
We implemented this application on a network of 2.3~GHz quad-core
AMD Opteron systems, deploying nodes $A$, $B$, and $C$ on one
system and node $D$ on a second system connected via Gigabit Ethernet.
Figure~\ref{fig:msgoverheads} shows the measured execution times
when generating a set of a thousand normally distributed random numbers
for both the Na\"ive Algorithm (in which a dummy message is sent
for every filtered input) and the Non-propagation Algorithm.
It is readily apparent that the decrease in dummy messages has
a real impact on the overall application performance (in this case
determined by the execution time of the system executing nodes
$A$, $B$, and $C$), with a performance gain that averages 16\%.

\begin{figure}[t]
\begin{center}
	\includegraphics[scale=0.25]{msgoverheads}
	\captionof{figure}{Mean measured execution time. Error bars
represent 95\% confidence intervals for 6 trials.}
	\label{fig:msgoverheads}
\end{center}
\end{figure}

To further investigate the connection between dummy message volume
and application performance, we also generated a micro-benchmark
application with the same topology (that of Figure~\ref{fig:splitjoin}).
This application was deployed on four systems, with each node
assigned to a unique system.
In this case, we instructed nodes $B$ and $C$ to filter messages
probabilistically (using Bernoulli trials set to filter 75\% of the inputs),
and measured the execution time impact on node $D$ to receive
messages (both real and dummy).  Table~\ref{tbl:microbench} shows
the number of dummy messages received and mean execution time as
a function of the dummy message interval for this micro-benchmark.

\begin{table}[ht]
\begin{center}
\caption{Micro-benchmark performance (4 million real msgs)}
\label{tbl:microbench}
{\small
\begin{tabular}{|l|c|c|c|c|}
\hline
Dummy Interval & 5 & 10 & 15 & 20 \\
\hline
Received Msgs & 1,672,332 & 1,160,039 & 1,073,049 & 1,053,892 \\
Avg. Time (s) & 11.18 & 9.88 & 9.57 & 8.73 \\
\hline
\end{tabular}
}
\end{center}
\end{table}

The results from the micro-benchmark tell a similar story.  The
volume of dummy messages can have a significant impact on the overall
application performance.
